The ACO Seminar (2020–2021)

Given a point set in $\mathbb{R}^d$ in general position, a convex $k$-hole is a $k$-element subset in convex position whose convex hull is empty inside. Erdős and Szekeres proved that there always exists a $k$-element subset in convex position if the size of given point set is large enough. However, for k large enough, it's not guaranteed to be a $k$-hole. In this talk, I'll talk about the constructions of sets without $k$-holes.

Please email Boris Bukh (bbukh ~at~ math) for a password.